A finite axiomatization of inductive-recursive denitions

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1581, Issue , 1999, Pages 129-146

  Dybjer, Peter ^a   Setzer, Anton ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

PATHOLOGY;

AXIOMATIZATION; HIGHER-ORDER; INDUCTIVE-RECURSIVE; RECURSIONS; SET-THEORETIC MODELS; STRUCTURAL RECURSION; TYPE THEORY;

BIOMINERALIZATION;

EID: 84949206194     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48959-2_11     Document Type: Conference Paper

References (26)

1. P. Dybjer. Inductive families. Formal Aspects of Computing, 6:440-465, 1994.
2. E. Palmgren. On universes in type theory. To appear in: G. Sambin, and J. Smith, editors: Twenty-Five Years of Constructive Type Theory.
3. P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, 1984.
4. P. Martin-Löf. An intuitionistic theory of types. In G. Sambin and J. Smith, editors, Twenty-Five Years of Constructive Type Theory. Oxford University Press, 1998. To appear. Reprinted version of an unpublished report from 1972.
5. P. Aczel. On relating type theories and set theories. Submitted to TYPES’ 98, LNCS, Springer-Verlag.
6. A. Setzer. A model for a type theory with Mahlo universe. Draft, 1996.
7. A. S. Troelstra. On the syntax of Martin-Löf’s type theories. Theoretical ComputerScience, 51:1-26, 1987.
8. A. Setzer. Well-ordering proofs for Martin-Löf type theory. Annals of Pure and Applied Logic, 92:113-159, 1998.
9. F. R. Drake. Set Theory - an Introduction to Large Cardinals. North Holland, 1974.
10. A. Setzer. Extending Martin-Löf Type Theory by one Mahlo-universe. To appear in Archive for Mathematical Logic.
11. P. F. Mendler. Predicative type universes and primitive recursion. In Proceedings Sixth Annual Synposium on Logic in Computer Science. IEEE Computer Society Press, 1991.
12. S. Allen. A Non-Type-Theoretic Semantics for Type-Theoretic Language. PhD thesis, Department of Computer Science, Cornell University, 1987.
13. E. Griffor and M. Rathjen. The strength of some Martin-Löf type theories. Archive for Mathematical Logic, 33:347-385, 1994.
14. T. Coquand and C. Paulin. Inductively defined types, preliminary version. In LNCS 417, COLOG '88, International Conference on Computer Logic. SpringerVerlag, 1990.
15. J. Cederquist. Pointfree Approach to Constructive Analysis in Type Theory. PhD thesis, Department of Computing Science, Chalmers University of Technology and University of Göteborg, 1997.
16. C. Paulin-Mohring. Inductive definitions in the system Coq - rules and properties. In Proceedings Typed λ-Calculus and Applications, pages 328-245. Springer-Verlag, LNCS, March 1993.
17. P. Martin-Löf. Hauptsatz for the intuitionistic theory of iterated inductive definitions. In J. E. Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, pages 179-216. North-Holland, 1971.
18. P. Dybjer. A general formulation of simultaneous inductive-recursive definitions in type theory. To appear in Journal of Symbolic Logic.
19. R. Backhouse. On the meaning and construction of the rules in Martin-Löf’s theory of types. In A. Avron, B. Harper, F. Honsell, I. Mason, and G. Plotkin, editors, Proceedings of the Workshop on General Logic, Edinburgh, February 1987. Laboratory for Foundations of Computer Science, Department of Computer Science, University of Edinburgh, 1988. ECS-LFCS-88-52.
20. P. Dybjer. Inductive sets and families in Martin-Löf’s type theory and their set-theoretic semantics. In G. Huet and G. Plotkin, editors, Logical Frameworks, pages 280-306. Cambridge University Press, 1991.
21. B. Nordström, K. Petersson, and J. Smith. Programming in Martin-Löf’s Type Theory: an Introduction. Oxford University Press, 1990.
22. E. Palmgren. On Fixed Point Operators, Inductive Definitions and Universes in Martin-Löf’s Type Theory. PhD thesis, Uppsala University, 1991.
23. M. Rathjen, E. R. Griffor, and E. Palmgren. Inaccessibility in constructive set theory and type theory. Annals of Pure and Applied Logic, 94:181-200, 1998.
24. A. Setzer. Proof theoretical strength of Martin-Löf Type Theory with W-type and one universe. PhD thesis, Fakultöt fur Mathematik der Ludwig-Maximilians-Universität München, 1993.
25. A. Setzer. An upper bound for the proof theoretical strength of Martin-Löf Type Theory with W-type and one Universe. Draft, 1996.
26. A. Setzer. Proof theoretical strength of Martin-Löf Type Theory with W-type and one universe. PhD thesis, Universität München, 1993.